[passion]

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Well this is a case where your theoretical optimal strategy under the assumption that both players are super rational actors is potentially flawed. If you run this game as an experiment many B's will reject offers that they don't feel are fair. This seems may seem irrational to people who only value the units and don't realize that people are not rational actors and that money isn't always a "good" or isn't always the only "good". Some people will turn the money down on a matter of principle.

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Of course I agree with you. If you run this as an experiment you you would not get the As offering Bs the smallest possible shares. That said, it is game theory so we are operating under the assumption that all the players care about is their payoffs. If all players care about is their payoffs, the equillibrium strategies for A to offer B the smallest share in every period and for B to accept.

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Also, even if people are relatively rational, B may be able to tell A and convince him that he'll reject any offer that is less than X% of the prize pool. If B follows through on it the first few times rejecting the offer will A continue to offer a 999-1 split? Should he? If B knows that A will change his behavior then B should have this spite strategy. But if A counters and says he'll always offer 999-1 no matter what and if B trusts this and if all B cares about is maximizing his own money and no outside values (like spite or fairness or whatnot) than the 999-1 split is the theoretical optimal. So again this is a case of theoretical optimal versus experimental optimal.

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Again its game theory so we must assume, in absence of other information, that all players care about is their discounted stream of payoffs. In the case where the game is played a known and finite number of periods Bs threats to not accept payouts are not credible because both players can clearly see what is going to happen in the last, second to last, third to last, ....., periods ect.

If the game is played an indefinite number or infinite number of periods then Bs threats will have some bite and you will get equillibrium strategies that involve the Bs getting offered a higher share.

My sense is that in an actual experiment (in the finite period game) the outcome would depend on the total amount of money to be divided in each period. If it where $1 then A, then the Bs are not likely to accept a 1% share. If it were say $1,000,000 then the Bs would gleefully accept a 1% share. It is easy to stand up for whats just and fair when it doesn't cost you anything.

Passion